Question

1. CC Car Wash specializes in car cleaning services. The services offered by the company, the exact service time, and the resources needed for each of them are described in the table following:

   Service	Description	Processing Time	Resource
   A. Wash	Exterior car washing and drying	10 minutes	1 automated washing machine
   B. Wax	Exterior car waxing	15 minutes	1 automated waxing machine
   C. Wheel Cleaning	Detailed cleaning of all wheels	16 minutes	1 employee
   D. Interior Cleaning	Detailed cleaning inside the car	20 minutes	1 employee

   The company offers the following packages to their customers:

   • Package 1: Includes only car wash (service A).

   • Package 2: Includes car wash and waxing (services A and B).

   • Package 3: Car wash, waxing, and wheel cleaning (services A, B, and C).

   • Package 4: All four services (A, B, C, and D).

   Customers of CC Car Wash visit the station at a constant rate (you can ignore any effects of variability) of 50 customers per day. Of these customers, 30 percent buy Package 1, 30 percent buy Package 2, 15 percent buy Package 3, and 25 percent buy Package 4. The mix does not change over the course of the day. The store operates 10 hours a day.

   f. What is the implied utilization rate for the employee at service C (wheel cleaning)? Round your answer to the nearest whole number and ignore the percentage sign. For example, if your answer is 0.45 or 45%, fill in 45; if your answer is 0.76 or 76%, fill in 76.

   Your answer is .

Answer 1

Demand rate per package:

Total arrival rate per day = 50 customers

Package type	% of arrival	Demand rate per day
P1	0.3	50*0.3 = 15
p2	0.3	50*0.3 = 15
p3	0.15	50*0.15 = 7.5
P4	0.25	12.5

Demand rate at the workstations:

	A	B	C	D
	P1 (15)
	P2 (15)	P2 (15)
	P3 (7.5)	P3 (7.5)	P3 (7.5)
	P4 (12.5)	P4 (12.5)	P4 (12.5)	P4 (12.5)
Total Demand per day	50	35	20	12.5

Determine flow rate and capacity of the workstation:

Workstation	A	B	C	D
Processing time per unit (p)	10	15	16	20
Resources (r)	1	1	1	1
Capacity/hr = (60/p) x r	60/10*1 = 6	4	3.75	3
Capacity/day = capacity/hr x 10 hours per day	6*10 = 60	40	37.5	30
Demand rate per day	50	35	20	12.5
flow rate = minimum (demand rate, capacity)	=min(60, 50) = 50	35	20	12.5
Utilization = Flow rate / capacity x 100	50/60 x 100 = 83%	88%	53%	42%

Utilization of the workstation C = 53%